Legendre polynomials (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Legendre polynomials" in English language version.

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10doi.org

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Magnus, Wilhelm; Oberhettinger, Fritz (1943). Formeln und Satze fur die speziellen Funktionen der Mathematischen Physik. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen. Vol. 52. Springer. ISBN 978-3-662-41656-3. MR 0022272. OCLC 1026897547. {{cite book}}: ISBN / Date incompatibility (help)
Gradshteyn, I. S.; Ryzhik, I. M. (2015). Table of Integrals, Series, and Products. Elsevier. ISBN 978-0-12-384933-5. MR 3307944.

archive.org

Jackson, J. D. (1999). Classical Electrodynamics (3rd ed.). Wiley & Sons. p. 103. ISBN 978-0-471-30932-1.{{cite book}}: CS1 maint: location missing publisher (link)

degruyter.com

"Sur les séries dont le terme général dépend de deux angles, et qui servent à exprimer des fonctions arbitraires entre des limites donnée". Journal für die reine und angewandte Mathematik (Crelles Journal). 1837 (17): 35–56. 1 July 1837. doi:10.1515/crll.1837.17.35. ISSN 0075-4102.
Bruns, H. (1881). "Zur Theorie der Kugelfunctionen". CRLL. 1881 (90): 322–328. doi:10.1515/crll.1881.90.322. ISSN 1435-5345.

doi.org

Ciftja, Orion (2022). "Integrals of Legendre Polynomials over half range and their relation to the electrostatic potential in hemispherical geometry". Results in Physics. 40: 105838. Bibcode:2022ResPh..4005838C. doi:10.1016/j.rinp.2022.105838.
Carlitz, L. (1961). "Some integrals containing products of legendre polynomials". Archiv Mathem. 12: 334–340. doi:10.1007/BF01650571.
"Sur les séries dont le terme général dépend de deux angles, et qui servent à exprimer des fonctions arbitraires entre des limites donnée". Journal für die reine und angewandte Mathematik (Crelles Journal). 1837 (17): 35–56. 1 July 1837. doi:10.1515/crll.1837.17.35. ISSN 0075-4102.
Mehler, F. G. (June 1881). "Ueber eine mit den Kugel- und Cylinderfunctionen verwandte Function und ihre Anwendung in der Theorie der Elektricitätsvertheilung". Mathematische Annalen (in German). 18 (2): 161–194. doi:10.1007/BF01445847. ISSN 0025-5831.
"II. On a type of spherical harmonics of unrestricted degree, order, and argument". Proceedings of the Royal Society of London. 59 (353–358): 189–196. 1896-12-31. doi:10.1098/rspl.1895.0075. ISSN 0370-1662.
Gasper, George (1975), Ross, Bertram (ed.), "Formulas of the dirichlet-mehler type", Fractional Calculus and Its Applications, Lecture Notes in Mathematics, vol. 457, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 207–215, doi:10.1007/bfb0067105, ISBN 978-3-540-07161-7, retrieved 2025-03-18
Doha, E. H. (1991-01-01). "The coefficients of differentiated expansions and derivatives of ultraspherical polynomials". Computers & Mathematics with Applications. 21 (2): 115–122. doi:10.1016/0898-1221(91)90089-M. ISSN 0898-1221.
Askey, Richard (November 1969). "Mehler's Integral for P_n (cos θ)". The American Mathematical Monthly. 76 (9): 1046–1049. doi:10.1080/00029890.1969.12000407. ISSN 0002-9890.
Bruns, H. (1881). "Zur Theorie der Kugelfunctionen". CRLL. 1881 (90): 322–328. doi:10.1515/crll.1881.90.322. ISSN 1435-5345.

dx.doi.org

Doha, E. H. (1991-01-01). "The coefficients of differentiated expansions and derivatives of ultraspherical polynomials". Computers & Mathematics with Applications. 21 (2): 115–122. doi:10.1016/0898-1221(91)90089-M. ISSN 0898-1221.

harvard.edu

ui.adsabs.harvard.edu

Ciftja, Orion (2022). "Integrals of Legendre Polynomials over half range and their relation to the electrostatic potential in hemispherical geometry". Results in Physics. 40: 105838. Bibcode:2022ResPh..4005838C. doi:10.1016/j.rinp.2022.105838.

neurips.cc

Voelker, Aaron R.; Kajić, Ivana; Eliasmith, Chris (2019). Legendre Memory Units: Continuous-Time Representation in Recurrent Neural Networks (PDF). Advances in Neural Information Processing Systems.

nist.gov

dlmf.nist.gov

"DLMF: §18.10 Integral Representations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials". dlmf.nist.gov. Retrieved 18 March 2025.
"DLMF: 14.15 Uniform Asymptotic Approximations".

researchgate.net

Leonard C. Maximon (1957). "A generating function for the product of two Legendre polynomials". Norske Videnskabers Selskab Forhandlinger. 29: 82–86.

royalsocietypublishing.org

"II. On a type of spherical harmonics of unrestricted degree, order, and argument". Proceedings of the Royal Society of London. 59 (353–358): 189–196. 1896-12-31. doi:10.1098/rspl.1895.0075. ISSN 0370-1662.

springer.com

link.springer.com

Mehler, F. G. (June 1881). "Ueber eine mit den Kugel- und Cylinderfunctionen verwandte Function und ihre Anwendung in der Theorie der Elektricitätsvertheilung". Mathematische Annalen (in German). 18 (2): 161–194. doi:10.1007/BF01445847. ISSN 0025-5831.
Gasper, George (1975), Ross, Bertram (ed.), "Formulas of the dirichlet-mehler type", Fractional Calculus and Its Applications, Lecture Notes in Mathematics, vol. 457, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 207–215, doi:10.1007/bfb0067105, ISBN 978-3-540-07161-7, retrieved 2025-03-18

tandfonline.com

Askey, Richard (November 1969). "Mehler's Integral for P_n (cos θ)". The American Mathematical Monthly. 76 (9): 1046–1049. doi:10.1080/00029890.1969.12000407. ISSN 0002-9890.

uni-frankfurt.de

edocs.ub.uni-frankfurt.de

Legendre, A.-M. (1785) [1782]. "Recherches sur l'attraction des sphéroïdes homogènes" (PDF). Mémoires de Mathématiques et de Physique, présentés à l'Académie Royale des Sciences, par divers savans, et lus dans ses Assemblées (in French). Vol. X. Paris. pp. 411–435. Archived from the original (PDF) on 2009-09-20.

uwaterloo.ca

compneuro.uwaterloo.ca

Voelker, Aaron R.; Kajić, Ivana; Eliasmith, Chris (2019). Legendre Memory Units: Continuous-Time Representation in Recurrent Neural Networks (PDF). Advances in Neural Information Processing Systems.

web.archive.org

Legendre, A.-M. (1785) [1782]. "Recherches sur l'attraction des sphéroïdes homogènes" (PDF). Mémoires de Mathématiques et de Physique, présentés à l'Académie Royale des Sciences, par divers savans, et lus dans ses Assemblées (in French). Vol. X. Paris. pp. 411–435. Archived from the original (PDF) on 2009-09-20.

worldcat.org

search.worldcat.org

Magnus, Wilhelm; Oberhettinger, Fritz (1943). Formeln und Satze fur die speziellen Funktionen der Mathematischen Physik. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen. Vol. 52. Springer. ISBN 978-3-662-41656-3. MR 0022272. OCLC 1026897547. {{cite book}}: ISBN / Date incompatibility (help)
"Sur les séries dont le terme général dépend de deux angles, et qui servent à exprimer des fonctions arbitraires entre des limites donnée". Journal für die reine und angewandte Mathematik (Crelles Journal). 1837 (17): 35–56. 1 July 1837. doi:10.1515/crll.1837.17.35. ISSN 0075-4102.
Mehler, F. G. (June 1881). "Ueber eine mit den Kugel- und Cylinderfunctionen verwandte Function und ihre Anwendung in der Theorie der Elektricitätsvertheilung". Mathematische Annalen (in German). 18 (2): 161–194. doi:10.1007/BF01445847. ISSN 0025-5831.
Szegő, Gábor (1975). Orthogonal polynomials (4th ed.). Providence: American Mathematical Society. ISBN 0821810235. OCLC 1683237.
"II. On a type of spherical harmonics of unrestricted degree, order, and argument". Proceedings of the Royal Society of London. 59 (353–358): 189–196. 1896-12-31. doi:10.1098/rspl.1895.0075. ISSN 0370-1662.
Doha, E. H. (1991-01-01). "The coefficients of differentiated expansions and derivatives of ultraspherical polynomials". Computers & Mathematics with Applications. 21 (2): 115–122. doi:10.1016/0898-1221(91)90089-M. ISSN 0898-1221.
Askey, Richard (November 1969). "Mehler's Integral for P_n (cos θ)". The American Mathematical Monthly. 76 (9): 1046–1049. doi:10.1080/00029890.1969.12000407. ISSN 0002-9890.
Bruns, H. (1881). "Zur Theorie der Kugelfunctionen". CRLL. 1881 (90): 322–328. doi:10.1515/crll.1881.90.322. ISSN 1435-5345.